GRAB (version 0.2.4)

CCT: Cauchy Combination Test for p-value aggregation

Description

Combines multiple p-values using the Cauchy distribution method, which provides analytical p-value calculation under arbitrary dependency structures.

Usage

CCT(pvals, weights = NULL)

Value

Single aggregated p-value combining all input p-values.

Arguments

pvals

Numeric vector of p-values to combine (each between 0 and 1). P-values equal to 1 are automatically adjusted to 0.999. P-values equal to 0 will cause an error.

weights

Numeric vector of non-negative weights for each p-value. If NULL, equal weights are used. Must have same length as pvals.

Details

The Cauchy Combination Test (CCT) transforms p-values using the inverse Cauchy distribution and combines them with specified weights. This method is particularly powerful because it:

• Works under arbitrary dependency structures

• Provides exact analytical p-values (no simulation needed)

• Maintains good power properties across different scenarios

Special Cases:

• If any p-value equals 0, returns 0 immediately

• P-values equal to 1 are adjusted to 0.999 with a warning

• Very small p-values (< 1e-16) receive special numerical treatment

References

Liu, Y., & Xie, J. (2020). Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures. Journal of the American Statistical Association, 115(529), 393-402. tools:::Rd_expr_doi("10.1080/01621459.2018.1554485")

Examples

# Basic usage with equal weights
pvalues <- c(0.02, 0.0004, 0.2, 0.1, 0.8)
CCT(pvals = pvalues)

# Usage with custom weights
weights <- c(2, 3, 1, 1, 1)
CCT(pvals = pvalues, weights = weights)